Final answer:
The area of the canvas needed to make the cylindrical and conical tent is approximately 10380.79 square meters, calculated by finding the surface area of both the cylinder and the cone using their respective formulas.
Step-by-step explanation:
To find the area of the canvas needed to make the tent, we need to calculate the surface area of both the cylindrical and conical parts of the tent. For the cylindrical part, the surface area is the circumference of the base multiplied by the height. For the conical part, we use the lateral surface area formula, which depends on the slant height and the radius of the base.
First, let's calculate the surface area of the cylindrical part: Surface Area of Cylinder = 2πrh = 2×(3.1415927)×(52.5m)×(4m) = approximately 1319.47 square meters.
Next, we calculate the lateral surface area of the conical part: Surface Area of Cone = πrl = π×(52.5m)×(55m) = approximately 9061.32 square meters.
Now we sum both areas to get the total area of canvas needed: Total Area = Surface Area of Cylinder + Surface Area of Cone = 1319.47m² + 9061.32m² = approximately 10380.79 square meters.
Therefore, the area of the canvas needed to make the tent is roughly 10380.79 square meters.